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General Statistics Null Hypothesis

1 What is the difference between a null hypothesis and an alternative hypothesis? Is the null hypothesis always the same as the verbal claim or assertion that led to the test?
Why or why not?

2 For each of the following pairs of null and alternative hypotheses, determine whether the pair would be appropriate for a hypothesis test. If a pair is deemed inappropriate, explain why.

a. H0: u > or = 10, H1: u < 10

b. H0: u = 30, H1: u not equal to 30

c. H0: u > 90, H1: u < or = 90

d. H0: u < or = 75, H1: u < or = 85

e. H0: x > or = 15, H1: x < 15

f. H0: x = 58, H1: x not equal to 58

3 For each of the following pairs of null and alternative hypotheses, determine whether the pair would be appropriate for a hypothesis test. If a pair is deemed inappropriate, explain why.

a. H0: pie > or = 0.30, H1: pie < 0.35

b. H0: pie = 0.72, H1: pie is not equal to 0.72

c. H0: Pie < or = 0.25, H1: pie > 0.25

d. H0: pie > or = 0.48, H1: pie > 0.48

e. H0: pie < or = 0.70, H1: pie > 0.70

f. H0: p > or = 0.65, H1: p < 0.65

4 On CNN and other news networks, guests often express their opinions in rather strong, persuasive, and sometimes frightening terms. For example, a scientist who strongly believes that global warming is taking place will warn us of the dire consequences (such as rising sea levels, coastal flooding, and global climate change) she foresees if we do not take her arguments seriously. If the
scientist is correct, and the world does not take her seriously, would this be a Type I error or a Type II error?
Briefly explain your reasoning.

5 Many law enforcement agencies use voice-stress analysis to help determine whether persons under interrogation are lying. If the sound frequency of a person's voice changes when asked a question, the presumption is that the person is being untruthful. For this situation, state the null and alternative hypotheses in verbal terms, then identify what would constitute a Type I error and a
Type II error in this situation.

Solution Preview

1 What is the difference between a null hypothesis and an alternative hypothesis? Is the null hypothesis always the same as the verbal claim or assertion that led to the test?
Why or why not?

Solution:

Main difference is that only null hypothesis can have equal sign. The direction of inequality in alternate hypothesis tells whether test is one-tailed or two tailed. If there is not equal sign in alternate hypothesis then is two-tailed test, if there is > or < sign then it is one-tailed test. We perform hypothesis testing to see whether we can reject or fail to reject null hypothesis.

Null hypothesis is not always the same as the verbal claim or assertion that led to the test.

Suppose we want to test that a drug reduces the bold pressure. Null hypothesis for this test will be there is no change in blood pressure as null hypothesis should have equal sign.

2 For each of the ...

Solution Summary

The general statistics null hypothesis and alternative hypothesis is examined.

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